{"id":"https://openalex.org/W2021771760","doi":"https://doi.org/10.1080/00207169608804488","title":"On the monotone convergence of multisplitting method for a class of systems of weakly nonlinear equations","display_name":"On the monotone convergence of multisplitting method for a class of systems of weakly nonlinear equations","publication_year":1996,"publication_date":"1996-01-01","ids":{"openalex":"https://openalex.org/W2021771760","doi":"https://doi.org/10.1080/00207169608804488","mag":"2021771760"},"language":"en","primary_location":{"id":"doi:10.1080/00207169608804488","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207169608804488","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5108103543","display_name":"Wang Deren","orcid":null},"institutions":[{"id":"https://openalex.org/I113940042","display_name":"Shanghai University","ror":"https://ror.org/006teas31","country_code":"CN","type":"education","lineage":["https://openalex.org/I113940042"]},{"id":"https://openalex.org/I148128674","display_name":"University of Shanghai for Science and Technology","ror":"https://ror.org/00ay9v204","country_code":"CN","type":"education","lineage":["https://openalex.org/I148128674"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Wang Deren","raw_affiliation_strings":["Department of Mathematics , Shanghai University of Science and Technology , Shanghai, 201800, P.R. China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Shanghai University of Science and Technology , Shanghai, 201800, P.R. China","institution_ids":["https://openalex.org/I148128674","https://openalex.org/I113940042"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103371129","display_name":"Bai Zhongzhi","orcid":null},"institutions":[{"id":"https://openalex.org/I24943067","display_name":"Fudan University","ror":"https://ror.org/013q1eq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I24943067"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bai Zhongzhi","raw_affiliation_strings":["Institute of Mathematics, Fuden University , Shanghai, 200433, P.R. China"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Fuden University , Shanghai, 200433, P.R. China","institution_ids":["https://openalex.org/I24943067"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050075410","display_name":"David Evans","orcid":"https://orcid.org/0009-0002-2834-6700"},"institutions":[{"id":"https://openalex.org/I143804889","display_name":"Loughborough University","ror":"https://ror.org/04vg4w365","country_code":"GB","type":"education","lineage":["https://openalex.org/I143804889"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"D.J. Evans","raw_affiliation_strings":["Parallel Algorithms Research Centre , Loughborough University of Technology , Loughborough, Leicestershire, Lell 3TU, U.K"],"affiliations":[{"raw_affiliation_string":"Parallel Algorithms Research Centre , Loughborough University of Technology , Loughborough, Leicestershire, Lell 3TU, U.K","institution_ids":["https://openalex.org/I143804889"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5108103543"],"corresponding_institution_ids":["https://openalex.org/I113940042","https://openalex.org/I148128674"],"apc_list":null,"apc_paid":null,"fwci":2.0234,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.8620526,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"60","issue":"3-4","first_page":"229","last_page":"242"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.984499990940094,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8086686134338379},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.7273550033569336},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7221984267234802},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.7200549840927124},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6241595149040222},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6000739336013794},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5197403430938721},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.496613085269928},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.46532341837882996},{"id":"https://openalex.org/keywords/correctness","display_name":"Correctness","score":0.4624747037887573},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.4239826798439026},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4171585738658905},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.41618454456329346},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1111578643321991},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10685503482818604},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08611023426055908}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8086686134338379},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.7273550033569336},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7221984267234802},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.7200549840927124},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6241595149040222},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6000739336013794},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5197403430938721},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.496613085269928},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.46532341837882996},{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.4624747037887573},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.4239826798439026},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4171585738658905},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.41618454456329346},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1111578643321991},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10685503482818604},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08611023426055908},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207169608804488","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207169608804488","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W1970261865","https://openalex.org/W2038785199","https://openalex.org/W2059356446","https://openalex.org/W2083883802","https://openalex.org/W2090963365","https://openalex.org/W2321653420","https://openalex.org/W2478091498","https://openalex.org/W3035235874","https://openalex.org/W4299512035"],"related_works":["https://openalex.org/W1489292980","https://openalex.org/W2795079910","https://openalex.org/W2951610245","https://openalex.org/W3037410748","https://openalex.org/W1430963189","https://openalex.org/W1974262772","https://openalex.org/W2049901819","https://openalex.org/W2052430123","https://openalex.org/W1983437306","https://openalex.org/W4387778523"],"abstract_inverted_index":{"In":[0],"this":[1,94],"paper,":[2],"we":[3,100],"set":[4],"up":[5],"a":[6,13],"parallel":[7],"matrix":[8,75],"multisplitting":[9,68],"iterative":[10],"method":[11,95],"for":[12],"class":[14],"of":[15,17,38,62,72,86,120],"system":[16],"weakly":[18],"nonlinear":[19],"equations,":[20],"Au":[21],"=":[22],"G(u),":[23],"A\u220aL(R":[24,76],"n),":[25],"G:R":[26],"n":[27,29,77],"\u2192R":[28],",":[30],"which":[31],"is":[32,51,96],"generally":[33],"resulted":[34],"from":[35],"the":[36,44,47,55,59,73,84,89,102,116],"discretization":[37],"many":[39],"classical":[40],"differential":[41],"equations.":[42],"For":[43],"new":[45],"method,":[46],"two-sided":[48],"approximation":[49],"property":[50],"deliberately":[52],"shown,":[53],"and":[54,69,111,118],"comparison":[56],"theorems":[57],"between":[58],"convergence":[60,91],"rates":[61],"different":[63],"multisplit-tings":[64],"as":[65,67],"well":[66],"single":[70],"splittings":[71],"coefficient":[74],")":[78],"are":[79],"given":[80],"in":[81,83],"detail":[82],"sense":[85],"monotonicity.":[87],"Therefore,":[88],"monotone":[90],"theory":[92],"about":[93],"thoroghly":[97],"established.":[98],"Finally,":[99],"apply":[101],"built":[103],"conclusions":[104],"to":[105,114],"several":[106],"special":[107],"but":[108],"very":[109],"important":[110],"practical":[112],"multisplittings":[113],"confirm":[115],"correctness":[117],"effectiveness":[119],"our":[121],"theory.":[122]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}